FIG. 14 shows a well-known fingerprint sensor package 10, which mainly comprises a substrate 11, a semiconductor chip 12 and an encapsulant 13. The substrate 11 has an upper surface 11a and a lower surface 11b and the semiconductor chip 12 having a fingerprint sensing surface 12a is disposed on the upper surface 11a of the substrate 11 and electrically connected with the substrate 11. The encapsulant 13 is formed on the upper surface 11a of the substrate 11 to encapsulate a portion of the semiconductor chip 12 and expose the fingerprint sensing surface 12a of the semiconductor chip 12. However, there is no electrostatic discharge device disposed in the known fingerprint sensor package 10, it is easy to cause short circuit problem on the fingerprint sensor package 10 because an electrostatic cannot be discharged via the electrostatic discharge device in this case when finger touches the fingerprint sensing surface 12a of the semiconductor chip 12.